Minimal polynomials of the modified de Bruijn sequences

It is well known that a de Bruijn sequence over F2F2 has the minimal polynomial (x+1)d(x+1)d, where 2n-1+n⩽d⩽2n-12n-1+n⩽d⩽2n-1. We study the minimal polynomials of the modified de Bruijn sequences.